基于时间依赖基本解的奇异边界法模拟二维狄利克雷边界标量波方程

奇异边界法是一个半解析边界配点强格式方法,具有无数值积分和无网格、编程容易以及数学简单等优点。本文首次将时间依赖基本解运用于奇异边界法,计算模拟二维标量波方程;结合确定源点强度因子的反插值技术,提出了二维狄利克雷边界标量波方程源点强度因子的一个经验公式;引进了解决波方程基本解G奇异性的一种无奇异积分处理方法。数值实验证明,基于时间依赖基本解的奇异边界法可精确高效地模拟二维狄利克雷边界标量波方程,在计算效率、精度、稳定性和适应性等方面有明显优势。

Singular boundary method based on time-dependent fundamental solution for 2D Scalar Wave Equation

The singular boundary method(SBM)is a recent boundary-type collocation method with the merits of being meshless, integration-free, mathematically simple, and easy-to-program. This study makes the first attempt to extend the SBM with time-dependent fundamental solution to scalar two-dimensional wave equation. By using the inverse interpolation technique, an empirical formula is proposed to determine the origin intensity factor of the time-dependent SBM for the two-dimensional wave equation with Dirichlet boundary condition. We also introduce a non-singular integral approach to address G singularity of fundamental solution. The numerical experiments demonstrate that the present scheme shows visible advantages in terms of the accuracy and efficiency.